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Standard XII

Physics

Centripetal Acceleration

A rod of dens...

Question

A rod of density $ρ$ and length $l = \frac{10}{3}$ m is suspended about one end and is surrounded by a liquid of density $2 ρ$ as shown. The rod is released from rest in horizontal position. Find the angular speed (in rad/s) of rod, , when it becomes vertical for first time. Take $g = 10 m / s^{2} .$ .___

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Solution

$F_{b} \frac{l}{2} - W \frac{l}{2} = (\frac{M l^{2}}{3}) ω^{2} 2 ρ V g \frac{l}{2} - V ρ g \frac{1}{2} = V ρ g \frac{1}{2} = \frac{V ρ l^{2} ω^{2}}{6} g = \frac{l ω^{2}}{3} ω = \sqrt{\frac{3 g}{l}} = 3 r a d / s$

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A rod of density ρ and length l=103m is suspended about one end and is surrounded by a liquid of density 2ρ as shown. The rod is released from rest in horizontal position. Find the angular speed (in rad/s) of rod, , when it becomes vertical for first time. Take g=10m/s2..___

Fbl2−Wl2=(Ml23)ω22ρVgl2−Vρg12=Vρg12=Vρl2ω26g=lω23ω=√3gl=3rad/s

$F_{b} \frac{l}{2} - W \frac{l}{2} = (\frac{M l^{2}}{3}) ω^{2} 2 ρ V g \frac{l}{2} - V ρ g \frac{1}{2} = V ρ g \frac{1}{2} = \frac{V ρ l^{2} ω^{2}}{6} g = \frac{l ω^{2}}{3} ω = \sqrt{\frac{3 g}{l}} = 3 r a d / s$